This book grew out of lectures presented to students of mathematics, physics, and mechanics by A. T. Fomenko at Moscow University, under the auspices of the Moscow Mathematical Society. The book describes modern and visual aspects of the theory of minimal, two-dimensional surfaces in three-dimensional space. The main topics covered are: topological properties of minimal surfaces, stable and unstable minimal films, classical examples, the Morse-Smale index of minimal two-surfaces in Euclidean spa...
Complex Geometry and Lie Theory (Proceedings of Symposia in Pure Mathematics)
In the late 1960s and early 1970s, Phillip Griffiths and his collaborators undertook a study of period mappings and variation of Hodge structure. The motivating problems, which centered on the understanding of algebraic varieties and the algebraic cycles on them, came from algebraic geometry. However, the techiques used were transcendental in nature, drawing heavily on both Lie theory and hermitian differential geometry. Promising approaches were formulated to fundamental questions in the theory...
An Introduction to Extremal Kahler Metrics (Graduate Studies in Mathematics)
by Gabor Szekelyhidi
A basic problem in differential geometry is to find canonical metrics on manifolds. The best known example of this is the classical uniformization theorem for Riemann surfaces. Extremal metrics were introduced by Calabi as an attempt at finding a higher-dimensional generalization of this result, in the setting of Kahler geometry. This book gives an introduction to the study of extremal Kahler metrics and in particular to the conjectural picture relating the existence of extremal metrics on proje...
Invariant Probalbilities of Markovfeller Operators and Their Supports (Frontiers in Mathematics)
by Radu Zaharopol
This book covers invariant probabilities for a large class of discrete-time homogeneous Markov processes known as Feller processes. These Feller processes appear in the study of iterated function systems with probabilities, convolution operators, and certain time series. From the reviews: "A very useful reference for researchers wishing to enter the area of stationary Markov processes both from a probabilistic and a dynamical point of view." --MONATSHEFTE FUER MATHEMATIK
Cr Submanifolds of Kaehlerian and Sasakian Manifolds (Progress in Mathematics, #30)
by Kentaro Yano and Masahiro Kon
The Geometry of Higher-Order Hamilton Spaces (Fundamental Theories of Physics, #132)
by R. Miron
Asisknown,theLagrangeandHamiltongeometrieshaveappearedrelatively recently [76, 86]. Since 1980thesegeometrieshave beenintensivelystudied bymathematiciansandphysicistsfromRomania,Canada,Germany,Japan, Russia, Hungary,e.S.A. etc. PrestigiousscientificmeetingsdevotedtoLagrangeandHamiltongeome- tries and their applications have been organized in the above mentioned countries and a number ofbooks and monographs have been published by specialists in the field: R. Miron [94, 95], R. Mironand M. Anastas...
Global Analysis of Minimal Surfaces
by Stefan Hildebrandt Ulrich Dierkes
Collected Papers - Gesammelte Abhandlungen (Springer Collected Works in Mathematics)
by Heinz Hopf
From the preface: "Hopf algebras, Hopf fibration of spheres, Hopf-Rinow complete Riemannian manifolds, Hopf theorem on the ends of groups - can one imagine modern mathematics without all this? Many other concepts and methods, fundamental in various mathematical disciplines, also go back directly or indirectly to the work of Heinz Hopf: homological algebra, singularities of vector fields and characteristic classes, group-like spaces, global differential geometry, and the whole algebraisation of t...
This book presents the discovery of non-Euclidean geometry and the subsequent reformulation of the foundations of Euclidean geometry. The book provides a selection of topics suitable for the undergraduate student. A feature of this text is that some new results are developed in the exercises and then built upon in subsequent chapters. Many new exercises have been included in this edition. The book incorporates a discussion of the historical development of ideas, and the philisophical implication...
Lectures on Minimal Surfaces: Volume 1, Introduction, Fundamentals, Geometry and Basic Boundary Value Problems
by Johannes C C Nitsche
Topology II (Encyclopaedia of Mathematical Sciences, #24)
by D. B. Fuchs and Oleg Ya. Viro
Two top experts in topology, O.Ya. Viro and D.B. Fuchs, give an up-to-date account of research in central areas of topology and the theory of Lie groups. They cover homotopy, homology and cohomology as well as the theory of manifolds, Lie groups, Grassmanians and low-dimensional manifolds. Their book will be used by graduate students and researchers in mathematics and mathematical physics.
Applied Differential Geometry
by Vladimir G Ivancevic and Tijana T Ivancevic
Gauge Theory and Symplectic Geometry (NATO Science Series C, #488)
Gauge theory, symplectic geometry and symplectic topology are important areas at the crossroads of several mathematical disciplines. The present book, with expertly written surveys of recent developments in these areas, includes some of the first expository material of Seiberg-Witten theory, which has revolutionised the subjects since its introduction in late 1994. Topics covered include: introductions to Seiberg-Witten theory, to applications of the S-W theory to four-dimensional manif...
The Global Theory of Minimal Surfaces in Flat Spaces (Lecture Notes in Mathematics, #1775) (C.I.M.E. Foundation Subseries, #1775)
by W H III Meeks, A. Ros, and H Rosenberg
In the second half of the twentieth century the global theory of minimal surface in flat space had an unexpected and rapid blossoming. Some of the classical problems were solved and new classes of minimal surfaces found. Minimal surfaces are now studied from several different viewpoints using methods and techniques from analysis (real and complex), topology and geometry. In this lecture course, Meeks, Ros and Rosenberg, three of the main architects of the modern edifice, present some of the mor...
"Finsler Geometry: An Approach via Randers Spaces" exclusively deals with a special class of Finsler metrics -- Randers metrics, which are defined as the sum of a Riemannian metric and a 1-form. Randers metrics derive from the research on General Relativity Theory and have been applied in many areas of the natural sciences. They can also be naturally deduced as the solution of the Zermelo navigation problem. The book provides readers not only with essential findings on Randers metrics but also t...
Discrete Differential Geometry (DDG) is an emerging discipline at the boundary between mathematics and computer science. It aims to translate concepts from classical differential geometry into a language that is purely finite and discrete, and can hence be used by algorithms to reason about geometric data. In contrast to standard numerical approximation, the central philosophy of DDG is to faithfully and exactly preserve key invariants of geometric objects at the discrete level. This process of...
The 2009 World Forecasts of Tufted Textile Floor Coverings of Nylon or Other Polyamides Export Supplies
by Philip M. Parker
A Perspective on Canonical Riemannian Metrics (Progress in Mathematics, #336)
by Giovanni Catino and Paolo Mastrolia
This book focuses on a selection of special topics, with emphasis on past and present research of the authors on "canonical" Riemannian metrics on smooth manifolds.On the backdrop of the fundamental contributions given by many experts in the field, the volume offers a self-contained view of the wide class of "Curvature Conditions" and "Critical Metrics" of suitable Riemannian functionals. The authors describe the classical examples and the relevant generalizations.This monograph is the winner of...
The Geometry of Spacetime (Undergraduate Texts in Mathematics)
by James J. Callahan
Hermann Minkowski recast special relativity as essentially a new geometric structure for spacetime. This book looks at the ideas of both Einstein and Minkowski, and then introduces the theory of frames, surfaces and intrinsic geometry, developing the main implications of Einstein's general relativity theory.
Quantitative Arithmetic of Projective Varieties (Progress in Mathematics, #277)
by Timothy D Browning
OverthemillenniaDiophantineequationshavesuppliedanextremelyfertilesource ofproblems. Their study hasilluminated everincreasingpoints ofcontactbetween very di?erent subject areas, including algebraic geometry, mathematical logic, - godictheoryandanalyticnumber theory. Thefocus ofthis bookisonthe interface of algebraic geometry with analytic number theory, with the basic aim being to highlight the ro le that analytic number theory has to play in the study of D- phantine equations. Broadly speaking...